*Other* than the built in SSAS backup mechanism?? You don't need MSSQL to backup an SSAS cube, in 08 (and 05 and to a lesser extent 2k) you can backup from within SSAS to an *.abf file. This can have compresion turned on and also be password protected.

If you want to schedule/automate this, and you don't have SQL Agent to do the timings, if you do have (say) cron or any other scheduler, you should be able to run XMLA against the SSAS instance to get the back up to run (ie script the execution of the backup).